I had a similar dilemma, but mainly driven from not wanting to remove my camera/tripod plate every time I wanted to wear it with a BlackRapid

A solution that works very well for me is the Swift Clamp from Acratech - the BlackRapid attaches through the eye (just like the normal BalckRapid fastener) and I can clamp on/remove it from my camera/tripod plate. Also, when mounted on the tripod, the camera doesn't have any straps hanging from it

At $150 it is not a cheap solution; I have seen similar (cheaper) solutions but they often rely on adopting their specific camera plates. I was already using Acratech camera plates and ballhead, and therefore had little interest in changing to another camera plate (even if it is Arca Swiss compatible)